Question
Solve the following equation and verify the answer: $\text{2x}-\frac{1}{2}=3$
✓
Answer
$\text{2x}-\frac{1}{2}=3$
$\Rightarrow\text{2x}=3+\frac{1}{2}$ (Transporting $-\frac{1}{2}$ to $R.H.S.)$
$\Rightarrow\text{2x}=\frac{7}{2}$
$\Rightarrow\frac{\text{2x}}{2}=\frac{7}{2}\times\frac{1}{2}$ (Dividing both sides by $2)$
$\Rightarrow\text{x}=\frac{7}{4}$
$\therefore\text{x}=\frac{7}{4}$ is a solution of the given equation.
Check: Substituting $\text{x}=\frac{7}{4}$ in the given equation,
we get $\text{L.H.S.}=2\times\frac{7}{4}-\frac{1}{2}$
$=\frac{7}{2}-\frac{1}{2}=\frac{6}{2}=3$ and $R.H.S. = 3$
$\therefore$ When $\text{x}=\frac{7}{4},$
we have $L.H.S. = R.H.S.$
$\Rightarrow\text{2x}=3+\frac{1}{2}$ (Transporting $-\frac{1}{2}$ to $R.H.S.)$
$\Rightarrow\text{2x}=\frac{7}{2}$
$\Rightarrow\frac{\text{2x}}{2}=\frac{7}{2}\times\frac{1}{2}$ (Dividing both sides by $2)$
$\Rightarrow\text{x}=\frac{7}{4}$
$\therefore\text{x}=\frac{7}{4}$ is a solution of the given equation.
Check: Substituting $\text{x}=\frac{7}{4}$ in the given equation,
we get $\text{L.H.S.}=2\times\frac{7}{4}-\frac{1}{2}$
$=\frac{7}{2}-\frac{1}{2}=\frac{6}{2}=3$ and $R.H.S. = 3$
$\therefore$ When $\text{x}=\frac{7}{4},$
we have $L.H.S. = R.H.S.$
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